Twelve identical machines, running continuously at the same constant rate, take $8$ days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by $2$ days?

2

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Solution

The correct option is C $4$
$4$ additional machines: Let the work rate of $1$ machine be $r$ . Then the work rate of $12$ machines is $12 r$ , and you can set up an RTW chart:
The shipment work is then $96 r$ . To figure out how many machines are needed to complete this work in $8 - 2 = 6 d a y s$ , set up another row and solve for the unknown rate:
Therefore, there are $\frac{96 r}{6} = 16 r$ machines in total, or $16 - 12 = 4$ additional machines.

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Twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by 2 days?

Twelve identical machines, running continuously at the same constant rate, take $8$ days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by $2$ days?